Optimization of surface-plasmon-enhanced magneto-optical effects

Nicolas Bonod; Raymond Reinisch; Evgueny Popov; Michel Nevière

doi:10.1364/JOSAB.21.000791

Journal of the Optical Society of America B
Vol. 21,
Issue 4,
pp. 791-797
(2004)
•https://doi.org/10.1364/JOSAB.21.000791

Optimization of surface-plasmon-enhanced magneto-optical effects

Nicolas Bonod, Raymond Reinisch, Evgueny Popov, and Michel Nevière

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Nicolas Bonod, Raymond Reinisch, Evgueny Popov, and Michel Nevière, "Optimization of surface-plasmon-enhanced magneto-optical effects," J. Opt. Soc. Am. B 21, 791-797 (2004)

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Abstract

Kretschmann prism couplers, including magneto-optical media such as Co, Fe, and Ni, allow enhancement of the magneto-optical response, such as conversion of light polarization, thanks to the resonant excitation of surface plasmons. Since these media have high losses, they support overdamped surface plasmons. A way to get high-quality surface-plasmon resonance is to use noble-metal/ferromagnetic-metal multilayer thin films. The question that arises is, which surface-plasmon resonance leads to the largest enhancement: is it the overdamped or the high-quality one? We show that the best optimization not only depends on the orientation of the magnetic field but also on the magneto-optical coefficients. The most effective enhancer of the magneto-optical effects is the high-quality surface plasmons for the transverse orientation and may be the overdamped surface plasmons for the polar and longitudinal ones. This applies when the noble metal is gold and the magneto-optical medium is cobalt.

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Magnetic Orientation	$\| Δ r^{ss} \|$	$\| Δ r^{pp} \|$	$\| Δ r^{sp} \| = \| Δ r^{ps} \|$
Polar	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$
	$e_{2} = 1.0 nm$	$e_{2} = 1.0 nm$	$e_{2} = 1.0 nm$
	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 0.0 nm$
	$\| Δ r^{ss} \| = 1.46 \times 10^{- 5}$	$\| Δ r^{pp} \| = 1.65 \times 10^{- 5}$	$\| Δ r^{sp} \| = \| Δ r^{ps} \| = 4.7345 \times 10^{- 3}$
	$θ_{r} = 47.8 \deg$	$θ_{r} = 54.9 \deg$	$θ_{r} = 50.9 \deg$
Longitudinal	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$
	$e_{2} = 5.7 nm$	$e_{2} = 5.7 nm$	$e_{2} = 5.7 nm$
	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 0.0 nm$
	$\| Δ r^{ss} \| = 4.719 \times 10^{- 4}$	$\| Δ r^{pp} \| = 4.9 \times 10^{- 6}$	$\| Δ r^{sp} \| = \| Δ r^{ps} \| = 2.2073 \times 10^{- 3}$
	$θ_{r} = 41.5 \deg$	$θ_{r} = 41.6 \deg$	$θ_{r} = 41.6 \deg$
Transverse	Too small values	$e_{1, opt} = 0.0 nm$	$\| Δ r^{sp} \| = \| Δ r^{ps} \| = 0$
	of $\| Δ r^{ss} \|$	$e_{2} = 5.7 nm$
		$e_{3, opt} = 17.9 nm$
		$\| Δ r^{pp} \| = 3.6962 \times 10^{- 3}$
		$θ_{r} = 43.7 \deg$

Magnetic Orientation	$\| Δ t^{ss} \|$	$\| Δ t^{pp} \|$	$\| Δ t^{sp} \|$	$\| Δ t^{ps} \|$
Polar	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$
	$e_{2} = 1.0 nm$	$e_{2} = 1.0 nm$	$e_{2} = 1.0 nm$	$e_{2} = 1.0 nm$
	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 47.5 nm$	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 0.0 nm$
	$\| Δ t^{ss} \| = 1.45 \times 10^{- 5}$	$\| Δ t^{pp} \| = 4.36 \times 10^{- 5}$	$\| Δ t^{sp} \| = 3.1263 \times 10^{- 3}$	$\| Δ t^{ps} \| = 1.08480 \times 10^{- 2}$
	$θ_{r} = 47.8 \deg$	$θ_{r} = 43.9 \deg$	$θ_{r} = 50.8 \deg$	$θ_{r} = 41.5 \deg$
Longitudinal	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$
	$e_{2} = 5.7 nm$	$e_{2} = 5.7 nm$	$e_{2} = 5.7 nm$	$e_{2} = 5.7 nm$
	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 29.0 nm$	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 0.0 nm$
	$\| Δ t^{ss} \| = 4.718 \times 10^{- 4}$	$\| Δ t^{pp} \| = 9.4 \times 10^{- 6}$	$\| Δ t^{sp} \| = 1.4594 \times 10^{- 3}$	$\| Δ t^{ps} \| = 4.3029 \times 10^{- 3}$
	$θ_{r} = 41.5 \deg$	$θ_{r} = 43.1 \deg$	$θ_{r} = 41.6 \deg$	$θ_{r} = 41.7 \deg$
Transverse	Too small values	$e_{1, opt} = 1.5 nm$	$\| Δ t^{sp} \| = 0$	$\| Δ t^{ps} \| = 0$
	of $\| Δ t^{ss} \|$	$e_{2} = 5.7 nm$
		$e_{3, opt} = 34.2 nm$
		$\| Δ t^{pp} \|$ $= 1.11946 \times 10^{- 2}$
		$θ_{r} = 43.4 \deg$

Magnetic Orientation	$\| Δ r^{ss} \|$	$\| Δ r^{pp} \|$	$\| Δ r^{sp} \| = \| Δ r^{ps} \|$
Polar	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$
	$e_{2} = 1.0 nm$	$e_{2} = 1.0 nm$	$e_{2} = 1.0 nm$
	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 0.0 nm$
	$\| Δ r^{ss} \| = 1.46 \times 10^{- 5}$	$\| Δ r^{pp} \| = 1.65 \times 10^{- 5}$	$\| Δ r^{sp} \| = \| Δ r^{ps} \| = 4.7345 \times 10^{- 3}$
	$θ_{r} = 47.8 \deg$	$θ_{r} = 54.9 \deg$	$θ_{r} = 50.9 \deg$
Longitudinal	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$
	$e_{2} = 5.7 nm$	$e_{2} = 5.7 nm$	$e_{2} = 5.7 nm$
	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 0.0 nm$
	$\| Δ r^{ss} \| = 4.719 \times 10^{- 4}$	$\| Δ r^{pp} \| = 4.9 \times 10^{- 6}$	$\| Δ r^{sp} \| = \| Δ r^{ps} \| = 2.2073 \times 10^{- 3}$
	$θ_{r} = 41.5 \deg$	$θ_{r} = 41.6 \deg$	$θ_{r} = 41.6 \deg$
Transverse	Too small values	$e_{1, opt} = 0.0 nm$	$\| Δ r^{sp} \| = \| Δ r^{ps} \| = 0$
	of $\| Δ r^{ss} \|$	$e_{2} = 5.7 nm$
		$e_{3, opt} = 17.9 nm$
		$\| Δ r^{pp} \| = 3.6962 \times 10^{- 3}$
		$θ_{r} = 43.7 \deg$

Magnetic Orientation	$\| Δ t^{ss} \|$	$\| Δ t^{pp} \|$	$\| Δ t^{sp} \|$	$\| Δ t^{ps} \|$
Polar	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$
	$e_{2} = 1.0 nm$	$e_{2} = 1.0 nm$	$e_{2} = 1.0 nm$	$e_{2} = 1.0 nm$
	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 47.5 nm$	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 0.0 nm$
	$\| Δ t^{ss} \| = 1.45 \times 10^{- 5}$	$\| Δ t^{pp} \| = 4.36 \times 10^{- 5}$	$\| Δ t^{sp} \| = 3.1263 \times 10^{- 3}$	$\| Δ t^{ps} \| = 1.08480 \times 10^{- 2}$
	$θ_{r} = 47.8 \deg$	$θ_{r} = 43.9 \deg$	$θ_{r} = 50.8 \deg$	$θ_{r} = 41.5 \deg$
Longitudinal	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$	$e_{1, opt} = 0.0 nm$
	$e_{2} = 5.7 nm$	$e_{2} = 5.7 nm$	$e_{2} = 5.7 nm$	$e_{2} = 5.7 nm$
	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 29.0 nm$	$e_{3, opt} = 0.0 nm$	$e_{3, opt} = 0.0 nm$
	$\| Δ t^{ss} \| = 4.718 \times 10^{- 4}$	$\| Δ t^{pp} \| = 9.4 \times 10^{- 6}$	$\| Δ t^{sp} \| = 1.4594 \times 10^{- 3}$	$\| Δ t^{ps} \| = 4.3029 \times 10^{- 3}$
	$θ_{r} = 41.5 \deg$	$θ_{r} = 43.1 \deg$	$θ_{r} = 41.6 \deg$	$θ_{r} = 41.7 \deg$
Transverse	Too small values	$e_{1, opt} = 1.5 nm$	$\| Δ t^{sp} \| = 0$	$\| Δ t^{ps} \| = 0$
	of $\| Δ t^{ss} \|$	$e_{2} = 5.7 nm$
		$e_{3, opt} = 34.2 nm$
		$\| Δ t^{pp} \|$ $= 1.11946 \times 10^{- 2}$
		$θ_{r} = 43.4 \deg$

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Equations (15)

Journal of the Optical Society of America B